Abstract

Let X be an infinite-dimensional real reflexive Banach
space with dual space X∗ and G⊂X open and bounded. Assume that X and X∗ are locally uniformly
convex. Let T:X⊃D(T)→2X∗ be maximal
monotone and C:X⊃D(C)→X∗ quasibounded and of
type (S˜+). Assume that L⊂D(C),
where L is a dense subspace of X, and 0∈T(0). A
new topological degree theory is introduced for the sum T+C. Browder's degree theory has thus been extended to
densely defined perturbations of maximal monotone operators
while results of Browder and Hess have been extended to
various classes of single-valued densely defined generalized
pseudomonotone perturbations C. Although the main results
are of theoretical nature, possible applications of the new
degree theory are given for several other theoretical
problems in nonlinear functional analysis.

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